IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v76y2012i1p272-284.html
   My bibliography  Save this article

Efficiency and stochastic stability in normal form games

Author

Listed:
  • Man, Priscilla T.Y.

Abstract

Standard evolutionary game models select the risk-dominant equilibrium, even if it is not efficient. On the other hand, Robson [Robson, A.J., 1990. Efficiency in evolutionary games: Darwin, Nash and the secret handshake. J. Theoret. Biol. 144, 379–396] argues that genes can achieve efficient outcomes with a payoff-irrelevant type, even if such outcomes are not Nash. This paper follows Robsonʼs approach but assumes that a more complex mutation in both the type and the behavior is an order of magnitude less likely than a simpler mutation in only the type or the behavior. In weakly acyclic games, every long-run stable strategy profile is a strict Nash equilibrium. Meanwhile, a Pareto undominated strict Nash equilibrium is stochastically stable if for each player, the opponentsʼ equilibrium action profile uniquely maximizes his payoff given his equilibrium action. These results can be generalized to generic cyclic two-person games. In a common interests game, a strategy profile is selected if and only if it yields the unique Pareto efficient payoff vector.

Suggested Citation

  • Man, Priscilla T.Y., 2012. "Efficiency and stochastic stability in normal form games," Games and Economic Behavior, Elsevier, vol. 76(1), pages 272-284.
  • Handle: RePEc:eee:gamebe:v:76:y:2012:i:1:p:272-284
    DOI: 10.1016/j.geb.2012.06.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825612000899
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.geb.2012.06.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ely Jeffrey C, 2002. "Local Conventions," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 2(1), pages 1-32, May.
    2. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, December.
    3. Glenn Ellison, 2000. "Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution," Review of Economic Studies, Oxford University Press, vol. 67(1), pages 17-45.
    4. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-1071, September.
    5. Peski, Marcin, 2010. "Generalized risk-dominance and asymmetric dynamics," Journal of Economic Theory, Elsevier, vol. 145(1), pages 216-248, January.
    6. Robson, Arthur J. & Vega-Redondo, Fernando, 1996. "Efficient Equilibrium Selection in Evolutionary Games with Random Matching," Journal of Economic Theory, Elsevier, vol. 70(1), pages 65-92, July.
    7. Ritzberger, Klaus & Weibull, Jorgen W, 1995. "Evolutionary Selection in Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1371-1399, November.
    8. Fudenberg, Drew & Imhof, Lorens A., 2008. "Monotone imitation dynamics in large populations," Journal of Economic Theory, Elsevier, vol. 140(1), pages 229-245, May.
    9. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    10. Matsui, Akihiko, 1991. "Cheap-talk and cooperation in a society," Journal of Economic Theory, Elsevier, vol. 54(2), pages 245-258, August.
    11. Hillas, John, 1990. "On the Definition of the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 58(6), pages 1365-1390, November.
    12. Wiseman, Thomas & Yilankaya, Okan, 2001. "Cooperation, Secret Handshakes, and Imitation in the Prisoners' Dilemma," Games and Economic Behavior, Elsevier, vol. 37(1), pages 216-242, October.
    13. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
    14. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    15. Hahn, Sunku, 2003. "The Long Run Equilibrium in a Game of "Battle of the Sexes"," Hitotsubashi Journal of Economics, Hitotsubashi University, vol. 44(1), pages 23-35, June.
    16. Dieter Balkenborg & Dries Vermeulen, 2016. "Where Strategic and Evolutionary Stability Depart—A Study of Minimal Diversity Games," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 278-292, February.
    17. Kim, Yong-Gwan & Sobel, Joel, 1995. "An Evolutionary Approach to Pre-play Communication," Econometrica, Econometric Society, vol. 63(5), pages 1181-1193, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Matros, Alexander & Moser, Scott, 2015. "Coordination in a changing environment," Journal of Economic Behavior & Organization, Elsevier, vol. 112(C), pages 64-84.
    2. Neary, Philip R., 2012. "Competing conventions," Games and Economic Behavior, Elsevier, vol. 76(1), pages 301-328.
    3. Weibull, Jörgen W., 1997. "What have we learned from Evolutionary Game Theory so far?," Working Paper Series 487, Research Institute of Industrial Economics, revised 26 Oct 1998.
    4. Ge Jiang & Simon Weidenholzer, 2017. "Local interactions under switching costs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(3), pages 571-588, October.
    5. Blume, Andreas, 1998. "Communication, Risk, and Efficiency in Games," Games and Economic Behavior, Elsevier, vol. 22(2), pages 171-202, February.
    6. Ennio Bilancini & Leonardo Boncinelli, 2018. "Social coordination with locally observable types," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(4), pages 975-1009, June.
    7. Ennio Bilancini & Leonardo Boncinelli, 2015. "Social coordination with locally observable types," Department of Economics 0051, University of Modena and Reggio E., Faculty of Economics "Marco Biagi".
    8. V. Masson, 2015. "Information, interaction and memory," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(4), pages 1015-1032, November.
    9. Norman, Thomas W.L., 2009. "Rapid evolution under inertia," Games and Economic Behavior, Elsevier, vol. 66(2), pages 865-879, July.
    10. Kosfeld, Michael, 2002. "Why shops close again: An evolutionary perspective on the deregulation of shopping hours," European Economic Review, Elsevier, vol. 46(1), pages 51-72, January.
    11. Ennio Bilancini & Leonardo Boncinelli, 2020. "The evolution of conventions under condition-dependent mistakes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(2), pages 497-521, March.
    12. Demichelis, Stefano & Ritzberger, Klaus, 2003. "From evolutionary to strategic stability," Journal of Economic Theory, Elsevier, vol. 113(1), pages 51-75, November.
    13. Alós-Ferrer, Carlos & Weidenholzer, Simon, 2014. "Imitation and the role of information in overcoming coordination failures," Games and Economic Behavior, Elsevier, vol. 87(C), pages 397-411.
    14. Vyrastekova, J., 2002. "Efficiency versus Risk Dominance in an Evolutionary Model with Cheap Talk," Other publications TiSEM 8af6c389-f8e1-429a-9841-6, Tilburg University, School of Economics and Management.
    15. Alós-Ferrer, Carlos & Weidenholzer, Simon, 2008. "Contagion and efficiency," Journal of Economic Theory, Elsevier, vol. 143(1), pages 251-274, November.
    16. Hsiao-Chi Chen & Yunshyong Chow & Li-Chau Wu, 2013. "Imitation, local interaction, and coordination," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(4), pages 1041-1057, November.
    17. Vyrastekova, J., 2002. "Efficiency versus Risk Dominance in an Evolutionary Model with Cheap Talk," Discussion Paper 2002-6, Tilburg University, Center for Economic Research.
    18. Pin, Paolo & Weidenholzer, Elke & Weidenholzer, Simon, 2017. "Constrained mobility and the evolution of efficient outcomes," Journal of Economic Dynamics and Control, Elsevier, vol. 82(C), pages 165-175.
    19. Matsui Akihiko & Matsuyama Kiminori, 1995. "An Approach to Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 65(2), pages 415-434, April.
    20. Wallace, Chris & Young, H. Peyton, 2015. "Stochastic Evolutionary Game Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.

    More about this item

    Keywords

    Secret handshake; Stochastic stability; Efficiency; Evolutionary game;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:gamebe:v:76:y:2012:i:1:p:272-284. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.